A071010 Sigma(k)/4 when k is not a sum of 2 squares.

1, 3, 2, 3, 7, 6, 6, 5, 8, 9, 6, 15, 10, 14, 18, 8, 12, 12, 15, 14, 24, 11, 21, 18, 12, 31, 18, 30, 18, 30, 20, 15, 42, 24, 26, 36, 17, 24, 36, 18, 31, 35, 24, 42, 20, 21, 56, 33, 30, 45, 28, 42, 32, 36, 30, 63, 39, 54, 26, 48, 27, 70, 54, 38, 62, 60, 36, 45, 36, 90, 42, 56, 78

Offset: 1

Author

Benoit Cloitre, May 19 2002

Keywords

• easy
• nonn

Comments

Conjecture : if n is not the sum of 2 squares sigma(n) == 0 (mod 4) (converse is not true : if sigma(n) == 0 (mod 4), n is sometimes the sum of 2 squares : sigma(65) = 84 == 0 (mod 4) but 65 = 49+16 is a sum of 2 squares).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203, A022544.

Programs

Mathematica

DivisorSigma[1, Select[Range[120], SquaresR[2, #] == 0 &]]/4  (* Amiram Eldar, May 13 2022 *)

PARI

for(n=0,200,if(sum(i=0,n,sum(j=0,i,if(i^2+j^2-n,0,1)))==0,print1(sigma(n)/4,",")))

Formula

a(n) = sigma(A022544(n))/4.